NCERT Class 10 Chapter 13 Probability CBSE Board Sample Problems Long Answer
Get top class preparation for CBSE right from your home: fully solved questions with step-by-step explanation- practice your way to success.
Question
In figure is shown a disc on which a player spins an arrow twice. The fraction a/b is formed, where ‘a’ is the number of sector on which arrow stops on the first and b is the number of the sector in which the arrow stops on second spin. On each spin, each sector has equal chance of selection by the arrow. Find the probability that the .
Solution
For , when , b cannot take any value
, b can take 1 value
, b can take 2 value, i.e. 1 and 2
, b can take 3 value, i.e. 1, 2, 3
, b can take 4 value, i.e. 1, 2, 3, 4
, b can take 5 value, i.e. 1, 2, 3, 4, 5
Total possible outcomes
Favourable outcomes
Question
A number x is selected at random from the numbers 1, 4, 9, 16 and another number is selected at random from the numbers 1, 2, 3, 4. Find the probability that the value of xy is more than 16.
Solution
x can be 1. 4. 9 or 16 and y can be 1, 2, 3 or 4.
Total number of cases of xy is 16.
Number of cases when xy is more than 16 is i.e. 6 cases.
P (value of xy more than 16)
Question
A number x selected at random from the numbers 1.2.3 and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16. Find the probability that product of x and y is less than 16.
Solution
x can be any one of 1. 2, 3 or 4 and y can be any one of 1, 4, 9 or 16.
Total number of cases of
Number of cases when product is less than 16 is i.e. 8 cases.
Required probability
Question
Ajar contains 54 marbles each of which is blue, green or white. The probability of selecting a blue marble at random from the jar is and the probability of selecting a green marble at random is . How many white marbles does the jar contain?
Solution
Let there be b blue, g green and w white marbles in the marbles in the jar. Then,
P (Selecting a blue marble) =
It ¡s given that the probability of selecting a blue marble is .
We have.
P (Selecting a green marble)
[P (Selecting a green marble) =]
Substituting the values of b and g in (i), we get
Question
A card is drawn from a well shuffled deck of cards
What are the odds in favour of getting spade?
What are the odds against getting a spade?
What are the odds in favour of getting a face card?
What are the odds in favour of getting a red king?
Solution
Total cards 52
Spade =13
Remaining cards 39
i. The odds in favour of getting spade 13
The odds is not in favour of getting spade 39
2. The odds against getting a spade 13
The odds not against getting a spade 39
3. The odds in favour of getting a face card 12
The odds not in favour of getting a face card 40
4. The odds in favour of getting a red king 2
The odds not in favour of getting a red king 50
Question
Pair of dice is rolled simultaneously. Find the probability of getting a
(a) Sum of 9 or 11 on the dice
(b) Product of 6 on the dice
Solution
P (sum 9 or 11)
P (product 6)
Question
From a deck of playing cards, all clubs, aces and jacks are removed. The deck is shuffled well and then a card is drawn out at random. What is the probability that the card drawn is (i) a queen (ii) a face card (iii) a red card?
Solution
Number of cards
P (Queen)
P (face card)
P (Red card)
Question
Two dice are rolled simultaneously. Find the probability of getting
(a) Total of 8 or 10
(b) Product 12
Solution
P (sum 8 or 10)
P (product 12)
Question
The king, queen and jack of clubs are removed from a deck of 52 playing cards and the well shuffled. One card is selected from the remaining cards. Find the probability of getting:
(i) A heart
(ii) A king
(iii) A club
Solution
No. of cards
P (heart)
P (king)
P (club)